Solving for Height in Horizontal Projectile Motion: 41 m/s, 23 m, g = -9.8m/s

In summary, the problem involves an arrow fired horizontally at 41 m/s that travels 23 m horizontally. From this information, and using the equations Vf = Vi + at, X = Xi + Vit + 1/2at^2, and Y = Yi + Vit + 1/2at^2, we can determine that it will take 4.2 seconds for the arrow to reach the ground and that it will have a height of 85.76 meters when it does so.
  • #1
NemoMnemosyne
6
0
This was an even numbered problem from the book so there are no answers to make sure I've done this correctly or not.

Homework Statement


An arrow fires horizontally at 41 m/s travels 23 m horizontally. From what height was it fired?

Vi = 41 m/s
a = g = -9.8m/s
x = 23m

Homework Equations


Vf = Vi + at
X = Xi + Vit + 1/2at^2
Y = Yi + Vit + 1/2at^2


The Attempt at a Solution



A.) Time to reach ground

Vf = Vi +at =>
Vf - Vi/a = t =>
0 - 41/-9.8 = 4.2s

B.) Height of Cliff
y = Vit + 1/2at^2 =>
y = 41(4.2) + 1/2(-9.8)(4.2^2) =>
y = 85.76m
 
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  • #2
Hi!
It appears you have got yourself into a bit of a muddle. The real trick with questions like this is to separate out all the x and y parameters (speed (initial, u, and final, v), acceleration (a), distance (s), time (t)).

So, in x, we have:

Vx = Ux = 41m/s
ax = 0 (nothing to accelerate the particle in the x plane)
sx = 23m
tx = ?

And in y,

Uy = 0
Vy = ?
ay = g = 9.8m/s/s
sy = what we want to find
ty = tx (can you see why?)

Now, clearly you want to know how long the arrow is in the air for. You haven't got enough information from the y variables, but you have plenty in x! It turns out you just need to do a simple speed = distance over time calculation.

See what you can do with this new info.
 
  • #3
You have the right set of equations but you are getting x and y directions mixed up. The arrow is fired horizontally and that horizontal velocity is unchanging. The initial velocity in the vertical direction is zero and changes constantly until impact.
 

1. What is horizontal projectile motion?

Horizontal projectile motion is the motion of an object that is projected horizontally and moves only under the influence of gravity.

2. What are the key factors that affect horizontal projectile motion?

The key factors that affect horizontal projectile motion are the initial velocity, the angle of projection, and the acceleration due to gravity.

3. How can the distance traveled by a horizontally projected object be calculated?

The distance traveled by a horizontally projected object can be calculated using the formula: distance = velocity x time.

4. Can the horizontal and vertical components of projectile motion be separated?

Yes, the horizontal and vertical components of projectile motion can be separated using vector analysis. The horizontal component is constant, while the vertical component is affected by gravity.

5. What is the maximum horizontal distance that can be achieved by a horizontally projected object?

The maximum horizontal distance that can be achieved by a horizontally projected object is when it is projected at a 45-degree angle. This distance is equal to the initial velocity squared divided by the acceleration due to gravity.

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